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Constant force acting on a particle

  1. Aug 22, 2016 #1
    1. The problem statement, all variables and given/known data
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    2. Relevant equations


    3. The attempt at a solution

    If I consider a coordinate system with the -Y axis along the direction of force and X axis along a line perpendicular to it (except the direction of velocity vector) then this problem is equivalent to the usual projectile motion problem where a particle is projected from an elevation horizontally ( i.e velocity perpendicular to gravity ) .

    So I can conclude that the path in the problem is parabolic i.e option b) which is indeed the given answer .

    Now , when I tried to find the equation of trajectory , I am a bit lost .

    In the usual X-Y coordinate system with 'm' representing the mass of the particle , we have ,

    ## x = 3t + \frac{1}{2}\frac{4}{m}t^2##

    ## y = 4t - \frac{1}{2}\frac{3}{m}t^2##

    I am finding it difficult to solve the above equations so as to get the relation between x and y .

    Any sincere help is very much appreciated .

    Thanks .
     

    Attached Files:

  2. jcsd
  3. Aug 22, 2016 #2

    blue_leaf77

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    Calculate ##3x+4y## to eliminate the quadratic terms in ##t##. Then solve this for ##t## and substitute for ##t## in either ##x(t)## or ##y(t)##. You should get a parabola tilted at 45 degrees.
     
  4. Aug 22, 2016 #3
    Fantastic ! :smile:

    But on expanding I get a term containing ##xy## . I have never really seen an ##xy## term in the usual parabola equations .
     
  5. Aug 22, 2016 #4

    blue_leaf77

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    The coupled terms like that in conic sections such as parabola is an indication that this curve is rotated at an angle from ##x## or ##y## axis.
     
  6. Aug 22, 2016 #5
    Interesting :cool: .

    Thanks a lot .
     
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